The function f(x)=x−[x] is just the fractional-part function, usually denoted {x}=x−⌊x⌋. On any open interval (n,n+1) (where n∈ℤ ), ⌊x⌋=n is constant, so f(x)=x−n is continuous there. At an integer x=n, the left- and right-hand limits disagree: As x⟶n−, f(x)=x−(n−1)⟶n−(n−1)=1. As x⟶n+, f(x)=x−n⟶0 (and f(n)=0 ). Hence each integer n is a jump discontinuity. Answer: the points of discontinuity are exactly the integers, ℤ.